In this paper we investigate the problem of thermal explosion in a two-phase polydisperse combustible mixture. The model for the radiative heating of droplets takes into account the semi transparency of the droplets. The numerical results of the analysis are applied to the modeling of thermal explosion in diesel engines. The current work presents a new, simplified model of the thermal explosion in a combustible gaseous mixture containing vaporizing fuel droplets of different radii (polydisperse). The polydispersity is modeled using a probability density function (PDF) that corresponds to the initial distribution of fuel droplets. An explicit expression of the critical condition for the thermal explosion limit is derived analytically and represents a generalization of the critical parameter of the classical Semenov theory.